Spakk'r
(page 31)

Some people (especially adults) have trouble with Spakk'r because they feel silly just trying to read the clues!

Here is a solution (November 2000) by Cory and Julia from Harrison Middle School in Yarmouth, ME; for Mrs.Jagolinzer's Math Think Lab class. This seems to be a pretty prolific class; another solution follows...

The first graders on Spakk'r are counting. They have four syllables that represent numbers: Ba, To, Ku, and Pa. We figured out that Ba=1, To=4, Ku=16, and Pa=64. The clues gave us excerpts of Spakk'r's number system. We wrote down the excerpts and found that some of them overlapped. One example is: batoto, babatoto, bababatoto, tototo, batototo. Another clue was babato, bababato, toto, batoto, babatoto.... These clues overlapped on the number "babato." The two clues put together have a range from babato, through batototo. We continued in this fashion until we had figured out a full range with all of the clues included.

From this we reasoned what the syllables meant. We saw: batoto, then babatoto. It went up by one ba, so we figured that ba was 1. If ba was 1, and the order from one is ba,baba,bababa,to this means that this represents 1,2,3 so the next number is 4. So we figured that to was 4. You add them like normal numbers. 1+1+1=Ba+Ba+Ba. So when you get to 7,bababato, the next number has to be 8. Since you can't use the same syllable more than three times in one number, you have to add another syllable to the sequence.

Toto is 8. You add one ba, then another ba, then another ba, then another to and so on. If you keep this up until you get to bababatototo you will find that you get to 15 with only ba's and to's. Since you can't go any higher, you need a new syllable. This would be ku. You can go on and on with the same process until you get to, bababatototokukuku which is 63. Then you need another syllable which is pa. Pa is 64. The highest number in the Spakk'r number system that you can write is bababatototokukukupapapa. This equals 265.

The answers to the questions on the clues are:

"How would you say 1‚ in Spakk'r?" ba.

"How would you say 50‚ in Spakk'r?" babakuku.

"What does batotoku mean?" 25.

"What does babato mean?" 6.

"How do you count in Spakk'r?" You count in Spakk'r like this: ba is 1, so you go ba, then baba, then bababa, etc. But you can only have 3 syllables at a time in the certain number, so 4 would have to be to. You use ba‚ to increase the number by one, to‚ to increase the number by 4, ku‚ to increase the number by 16, and pa‚ to increase the number by 64.

(November, 2000) Same class of Mainiacs, this time Sarah and Heather:

We started with the clue in which the first graders are counting "babato, bababato, toto, batoto, babatoto," We figured that since in the beginning you just add a ba to each number in the sequence ba must be the equivalent of one. We then noticed that after every three bas, where there would have been four bas, the first graders then replaced the bas‚ with a to. This concluded that to‚ must be equal to four. We had finished with all but the question on that clue so we went to another clue to figure out what ku was. The next clue that we picked was the one where the first grader were counting "bababatototo, ku, baku, babaku, bababaku, toku," We observed that after bababatototo‚ came ku. Since bababatototo was equal to fifteen we decided that ku was equal to sixteen. With this information we were able to figure out that pa would be the equivalent of one plus three bas, three tos, and three kus‚ because in the clues they only use a number three times, so pa‚ is 64.

The questions and answers that were asked on the Spakk'r clues:

Q= How do you count in Spakk'r?

A= The numbers that are represented in the counting are square roots of four. ex. batotokupa = 89, ba = 1(4 to the 0), to = 4(4 to the 1), ku = 16(4 to the 2), and pa = 64(4 to the 3).

Q= How would you say 1 in Spakk'r?

A= ba

Q= What does babato mean?

A= 6

Q= What does batotoku mean?

A= 25

Q= How would you say 50 in Spakk'r?

A= babakukuku

Well! What a couple of thorough explanations! I hope, readers, that you take the time to go through the whole thing and not just look for the answers. There are even (very small) mistakes in them -- see if you can find them!

and now, just as I was finishing putting this on the wen, I get email from Emily, Elizabeth, and Sarah in the same class, with another solution for Spakk'r. I hope you understand if I don't put yours up right here (it's every bit as wonderful, and at least one of the mistakes is not there!).

Those prolific eighth-graders at Monroe City Middle School in Monroe City, MO sent me this:

Megan, Ashley, Matthew, Joslynn, and Jennifer, from Monroe City, Missouri have figured out the SPAKK'R problem. They say it wasn't as hard as GEAP,but was easier than ZNORLIAN.

The answers are:

What is one? ba

What does babato mean? 6

How would you say 50 in SPAKK'R? babakukuku

What does batotoku mean? 25

 

ba=1
to=four ba's=4
ku=four to's=16
pa=four ku's=64

 

teacher: Mrs. Barbara Carson, Monroe City Middle School

eeps comments: thank you for your solutions! Again, I don't guarantee that solutions are correct just because I post them :) But this looks pretty compelling.

In general, I'd love to get solutions with your reasoning attached. It can be tedious to write it all out, but even if you told us just a part of it, people who were confused might be able to follow in your footsteps!

What would be the next number you would need a new syllable for?

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